Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1360 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊#10624382 | C2 | semidirect |
| 2. C22×C22⋊#10624382 | C2 | semidirect |
| 3. C22×C4×#10624382 | C2 | semidirect |
| 4. #26042231 | C2 | direct (N × H) |
| 9. C2×C4⋊#10624382 | C22 | semidirect |
| 11. C2×C22⋊#10624382 | C22 | semidirect |
| 13. C2×C4×#10624382 | C22 | semidirect |
| 15. C22×D724 | C4 | semidirect |
| 16. C22×C22⋊D181 | C4 | semidirect |
| 19. C2×D4×D181 | C4 | semidirect |
| 22. C22×D4×C181 | C4 | semidirect |
| 27. C22×#10624382 | D4 | semidirect |
| 42. C2×D724 | C2×C4 | semidirect |
| 44. C2×C22⋊D181 | C2×C4 | semidirect |
| 55. C2×D4×C181 | C2×C4 | semidirect |
| 63. C2×#10624382 | C2×D4 | semidirect |
| 84. C2×Dic181 | C22⋊C4 | semidirect |
| 86. C4×D181 | C22⋊C4 | semidirect |
| 94. C2×C4×C181 | C22⋊C4 | semidirect |
| 120. C4×C181 | C2×C22⋊C4 | semidirect |
| 121. Dic181 | C2×C22⋊C4 | semidirect |
| 123. C2×C181 | #390 | semidirect |
| 127. D181 | #390 | semidirect |
| 131. C181 | C2×#390 | semidirect |
| 145. C22×D4 | #10624382 | semidirect |
| 172. C2×D4 | C2×#10624382 | semidirect |
| 226. C2×C4 | C22⋊#10624382 | semidirect |
| 253. C4 | C2×C22⋊#10624382 | semidirect |
| 260. C2 | #26042231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10624382 | 2 |
| C22×C22⋊#10624382 | 2 |
| C22×C4×#10624382 | 2 |
| #26042231 | 2 |
| C22×D4×D181 | 2 |
| C2×#390 | 181 |